Nonquasineutral relativistic current filaments and their X-ray emission

Nonquasineutral electron current filaments with the azimuthal magnetic field are considered that arise due to the generation of electron vorticity in the initial (dissipative) stage of evolution of a current-carrying plasma, when the Hall number is small (σB/en _e c ? 1) because of the low values of the plasma conductivity and magnetic field strength. Equilibrium filamentary structures with both zero and nonzero net currents are considered. Structures with a zero net current type form on time scales of t < t _sk = (r ₀ω _pe /c)² t _st, where t _sk is the skin time, t _st is the typical time of electron-ion collisions, and r ₀ is the radius of the filament. It is shown that, in nonquasineutral filaments in which the current is carried by electrons drifting in the crossed electric (E _r ) and magnetic (B _θ) fields, ultrarelativistic electron beams on the typical charge-separation scale r _B = B/(4πen _e ) (the so-called magnetic Debye radius) can be generated. It is found that, for comparable electron currents, the characteristic electron energy in filaments with a nonzero net current is significantly lower than that in zero-net-current filaments that form on typical time scales of t < t _sk. This is because, in the latter type of filaments, the oppositely directed electron currents repel one another; as a result, both the density and velocity of electrons increase near the filament axis, where the velocities of relativistic electrons are maximum. Filaments with a zero net current can emit X rays with photon energies ? ω up to 10 MeV. The electron velocity distributions in filaments, the X-ray emission spectra, and the total X-ray yield per unit filament length are calculated as functions of the current and the electron number density in the filament. Analytical estimates of the characteristic lifetime of a radiating filament and the typical size of the radiating region as functions of the plasma density are obtained. The results of calculations are compared with the available experimental data.     

Nonquasineutral model of an equilibrium Z-pinch

A fundamentally new approach is proposed for describing Z-pinches when the pinch current is gov-erned to a large extent by strong charge separation, which gives rise to a radial electric field in the nonquasineutral core of the pinch. In the central pinch region with a characteristic radius of about $r_0 \sim \sqrt {J_0 /en_e c}$ , part of the total pinch current J ₀<J, is carried by the drifting electrons and the remaining current is carried by ions moving at the velocity v _iz ～c(2eZJ/m _i c ³) in the peripheral region with a radial size of c/ω_pi. In the nonquasineutral core of a Z-pinch, the radial ion “temperature” is on the order of ZeJ ₀/c. The time during which the non-quasineutral region exists is limited by Coulomb collisions between the ions oscillating in the radial direction and the electrons. Since the magnetic field is not frozen in the ions, no sausage instability can occur in the non-quasineutral core of the Z-pinch. In the equilibrium state under discussion, the ratio of the radial charge-separation electric field E ₀ to the atomic field E _a may be as large as $E_0 /E_a \sim 137^2 (a_0 \omega _{pe} /c)\sqrt {J/J_{Ae} }$ , where a ₀ is the Bohr radius.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Formation of nonquasineutral vortex plasma structures with a zero net current

A nonquasineutral vortex structure with a zero net current is described that arises as a result of electron drift in crossed magnetic and electric fields, the latter being produced by charge separation on a spatial scale of about the magnetic Debye radius r _B = |B|/(4πen _e ). In such a structure with a radius of r ～ r _B , the magnetic field is maintained by a drift current on the order of the electron Alfvén current J _Ae = m _e c ³/(2e) and can become as strong as B ? m _e c ²/(er). Estimates show that, in a plasma with a density of n _e = 10²¹?10²³ cm^?3 and with nonzero electron vorticity driven by high-power laser radiation on a time scale on the order of θ _pe ^?1 , magnetic fields with a strength of B ～ 10⁸?10⁹ G are generated on micron and submicron scales. The system with closed current that is considered in the present paper can also serve as a model of hot spots in the channel of a Z-pinch.     

Existence and stability of equilibria in age-structured population dynamics

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.     

Conformational equilibria of valine studied by dynamics simulation.

The conformational probability distribution of a valine residue in the valine dipeptide and of the valine side chain in an alpha-helix, as well as the change in helix stability for replacing alanine with valine, has been calculated by molecular dynamics simulations of explicitly hydrated systems: dipeptide, tetrapeptide and 10-, 14- and 18-residue oligoalanine helices. All computed free-energy differences are means from at least eight separate slow-growth simulations, four in each direction and are reported with their root-mean-square deviations. Different values for the change in free energy of folding (delta delta G degrees) have been calculated with the use of forcefields having an all-atom and a central-atom representation of methyl groups, etc. The value obtained with the all-atom forcefield agrees well with new experimental values (3 kJ/mol = 0.7 kcal/mol). Furthermore, the most stable valine side-chain rotamer in the helix is different for these two representations. The most stable rotamer for the all atom conformation is the same one that predominates for valines in alpha-helices in proteins of known conformation. The lower conformational freedom of the valine side chain in the helix contributes 1 kJ/mol to the difference in stability computed with the all-atom potential; unfavorable interactions of the side chain with helix, even in the most stable conformation, further increase delta delta G degrees.     

Study of the dynamics of a plasma current sheath in the KPF-4 Phoenix plasma-focus facility

The engineering characteristics of the KPF-4 Phoenix megajoule Mather-type plasma focus facility constructed at the Sukhumi Physicotechnical Institute are described. Results from preliminary studies of the plasma dynamics at a capacitive-storage energy of up to 700 kJ are discussed. Future experiments in KPF-4 will be oriented at technological applications and will complement the studies carried out in the 2.8-MJ Filippovtype PF-3 plasma focus facility at the Nuclear Fusion Institute of the Russian Research Centre Kurchatov Institute.     

Experimental studies of the magnetic structure and plasma dynamics in current sheets (a review)

Based on measurements of magnetic fields in current sheets, spatial distributions of the electric current and electrodynamic forces in successive stages of the sheet evolution are determined. Two new effects manifesting themselves mostly in the late stages of the current sheet evolution have been discovered, namely, expansion of the current flow region at the periphery of the sheet and the appearance of a region with inverse currents, which gradually expands from the periphery toward the center of the sheet. Using spectroscopic methods, generation of superthermal plasma flows accelerated along the sheet width from the center toward the periphery has been revealed and investigated. The measured energies of accelerated plasma ions satisfactorily agree with the Ampère forces determined from magnetic measurements. The excitation of inverse currents additionally confirms the motion of high-speed plasma flows from the center of the current sheet toward its side edges.     

Evolutionary dynamics of finite populations in games with polymorphic fitness equilibria

The hawk-dove (HD) game, as defined by Maynard Smith [1982. Evolution and the Theory of Games. Cambridge University Press, Cambridge], allows for a polymorphic fitness equilibrium (PFE) to exist between its two pure strategies; this polymorphism is the attractor of the standard replicator dynamics [Taylor, P.D., Jonker, L., 1978. Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145-156; Hofbauer, J., Sigmund, K., 1998. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge] operating on an infinite population of pure-strategists. Here, we consider stochastic replicator dynamics, operating on a finite population of pure-strategists playing games similar to HD; in particular, we examine the transient behavior of the system, before it enters an absorbing state due to sampling error. Though stochastic replication prevents the population from fixing onto the PFE, selection always favors the under-represented strategy. Thus, we may naively expect that the mean population state (of the pre-absorption transient) will correspond to the PFE. The empirical results of Fogel et al. [1997. On the instability of evolutionary stable states. BioSystems 44, 135-152] show that the mean population state, in fact, deviates from the PFE with statistical significance. We provide theoretical results that explain their observations. We show that such deviation away from the PFE occurs when the selection pressures that surround the fitness-equilibrium point are asymmetric. Further, we analyze a Markov model to prove that a finite population will generate a distribution over population states that equilibrates selection-pressure asymmetry; the mean of this distribution is generally not the fitness-equilibrium state.     

3nion-independent conformational ordering in iota-carrageenan: Disorder-order equilibria and dynamics

The equilibria and dynamics of the disorder-to-order transition of the anionic polysaccharide iota-carrageenan have been studied in the presence of tetramethyl-ammonium salts. By the use of a stopped-flow polarimeter, the rate equation and temperature dependence of the observed forward rate-constant were found to accord with a co-operative dimerisation process. Activation parameters for helix nucleation were shown to be independent of the anion for solutions containing tetramethylammonium chloride and bromide, i.e., ΔH^‡ = 1 ±3 kJ.mol⁻¹, ΔS^‡ = −178 ±10 J.mol⁻¹.K⁻¹, ΔG^‡_298K = 54 ±2 kJ.mol⁻¹, and k_nuc,298K = 1880 ±80 dm³.mol⁻¹.s⁻¹. The temperature dependence of optical rotation was also shown to be independent of the anion present.     

Solid-state NMR approaches to measure topological equilibria and dynamics of membrane polypeptides

Biological membranes are characterized by a high degree of dynamics. In order to understand the function of membrane proteins and even more of membrane-associated peptides, these motional aspects have to be taken into consideration. Solid-state NMR spectroscopy is a method of choice when characterizing topological equilibria, molecular motions, lateral and rotational diffusion as well as dynamic oligomerization equilibria within fluid phase lipid bilayers. Here we show and review examples where the ¹⁵N chemical shift anisotropy, dipolar interactions and the deuterium quadrupolar splittings have been used to analyze motions of peptides such as peptaibols, antimicrobial sequences, Vpu, phospholamban or other channel domains. In particular, simulations of ¹⁵N and ²H-solid-state NMR spectra are shown of helical domains in uniaxially oriented membranes when rotation around the membrane normal or the helix long axis occurs.     

Surviving background extinction: Inferences from historic and current dynamics in the contrasting population structures of two endemic Mexican cycads

Ecological and microevolutionary perspectives were used to investigate signs of background extinction in two endemic species. We studied relict populations of the cycad Dioon caputoi, contrasting its population structure and neighborhood size with those of Dioon planifolium as a demographically healthier reference population. Population dynamics analysis was performed on two populations of D. caputoi through Integral Projection Models and genetic neighborhoods compared between species through 172 Inter Simple Sequence Repeat loci performed in one population of each of the two study species. The D. caputoi populations mostly comprised adult plants, while D. planifolium presented mainly juvenile individuals. Dioon caputoi showed equilibrium in population growth (i.e., λ ≈ 1), with low recruitment, and its genetic neighborhood revealed highly related individuals in a unique distance class (r_ij = 0.407, 33 m). A contrasting pattern was found in D. planifolium, which showed higher relatedness in the first distance class (r_ij = 0.543, 5 m), gradually decreasing to 20 m. The discrepancies between the two species reflect different strategies of persistence. Dioon caputoi conserves a relict dynamics with signs of a multigenerational, attritional loss of reproductive fitness, while D. planifolium does not. This study furthers our understanding of the background extinction process and the information will thus contribute to the management and conservation of this endangered species.     

Periodic thermomagnetic structures in solar plasma

Stationary solutions in the form of small-scale periodic cells in a plane perpendicular to the magnetic field are obtained in the framework of two-fluid magnetohydrodynamics. The solutions are established as a result of the development of thermal instability and represent a superposition of standing temperature waves. In solving the problem, an expression is used for a generalized heat source (including heating and radiative cooling) that forms a temperature transition region between the chromosphere and corona.     

Oligoglycine surface structures: molecular dynamics simulation

The full-atomic molecular dynamics (MD) simulation of adsorption mode for diantennary oligoglycines [H-Gly4-NH(CH2)5]2 onto graphite and mica surface is described. The resulting structure of adsorption layers is analyzed. The peptide second structure motives have been studied by both STRIDE (structural identification) and DSSP (dictionary of secondary structure of proteins) methods. The obtained results confirm the possibility of polyglycine II (PGII) structure formation in diantennary oligoglycine (DAOG) monolayers deposited onto graphite surface, which was earlier estimated based on atomic-force microscopy measurements.     

164 Extracting dynamics information from multiple structures

Meaningful dynamics information can be extracted from multiple experimental structures of the same, or closely related, proteins or RNAs. The covariance matrix of atom positions is decomposable into its principal components, and in this way, it is possible to rank-order the changes in the set of structures, and to determine what the most significant changes are. Usually, only a few principal components dominate the motions of the structures, and these usually relate to the functional dynamics. This dynamics information provides strong evidence for the plasticity of protein and RNA structures, and also suggests that these structures almost always have a highly limited repertoire of motions. In some cases, such as HIV protease, the dominant motions are opening and closing over the active site. For myoglobin, the changes are much smaller, reflecting in part the small changes in sequence, but nonetheless they show characteristic details that depend on the species. Sets of structures can also be used to derive the effective microscopic forces that are forcing a given conformational transition.     

Studies of plasma dynamics in megampere X-pinches

Results are presented from experimental studies of the dynamics and parameters of the plasma generated by megampere (up to 2.3 MA) currents flowing through X-pinches formed from crossed wires made of various materials. The experiments were performed with different numbers of wires and different wire diameters. The X-ray yield in neon-like molybdenum lines (in the 2.5- to 3-keV photon energy range) from a <20 μm hot spot was larger than 10 J, and the soft X-ray power emitted from this spot reached 120 GW. The hot-spot lifetime estimated by comparing the measured and calculated emission intensities and line profiles of helium-like Fe and Cr ions was ～10 ps. Hard X-ray emission in the photon energy range ≥800 keV was also detected.